/*
Copyright (c) 2010-2016, Mathieu Labbe - IntRoLab - Universite de Sherbrooke
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in the
      documentation and/or other materials provided with the distribution.
    * Neither the name of the Universite de Sherbrooke nor the
      names of its contributors may be used to endorse or promote products
      derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "rtabmap/core/Graph.h"

#include <rtabmap/utilite/ULogger.h>
#include <rtabmap/utilite/UStl.h>
#include <rtabmap/utilite/UMath.h>
#include <rtabmap/utilite/UConversion.h>
#include <rtabmap/utilite/UTimer.h>
#include <set>

#include <rtabmap/core/optimizer/OptimizerGTSAM.h>

#ifdef RTABMAP_GTSAM
#include <gtsam/geometry/Pose2.h>
#include <gtsam/geometry/Pose3.h>
#include <gtsam/inference/Key.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/slam/PriorFactor.h>
#include <gtsam/slam/BetweenFactor.h>
#include <gtsam/sam/BearingRangeFactor.h>
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <gtsam/nonlinear/GaussNewtonOptimizer.h>
#include <gtsam/nonlinear/DoglegOptimizer.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/nonlinear/NonlinearOptimizer.h>
#include <gtsam/nonlinear/Marginals.h>
#include <gtsam/nonlinear/Values.h>
#include "gtsam/GravityFactor.h"
#include <optimizer/gtsam/XYFactor.h>
#include <optimizer/gtsam/XYZFactor.h>
#include <gtsam/nonlinear/ISAM2.h>

#ifdef RTABMAP_VERTIGO
#include "vertigo/gtsam/betweenFactorSwitchable.h"
#include "vertigo/gtsam/switchVariableLinear.h"
#endif
#endif // end RTABMAP_GTSAM

namespace rtabmap {

OptimizerGTSAM::OptimizerGTSAM(const ParametersMap & parameters) :
	Optimizer(parameters),
	internalOptimizerType_(Parameters::defaultGTSAMOptimizer()),
	isam2_(0),
	lastSwitchId_(1000000000)
{
	lastRootFactorIndex_.first = 0;
	parseParameters(parameters);
}

OptimizerGTSAM::~OptimizerGTSAM()
{
#ifdef RTABMAP_GTSAM
	delete isam2_;
#endif
}

bool OptimizerGTSAM::available()
{
#ifdef RTABMAP_GTSAM
	return true;
#else
	return false;
#endif
}

void OptimizerGTSAM::parseParameters(const ParametersMap & parameters)
{
	Optimizer::parseParameters(parameters);
#ifdef RTABMAP_GTSAM
	Parameters::parse(parameters, Parameters::kGTSAMOptimizer(), internalOptimizerType_);

	bool incremental = isam2_;
	double threshold = Parameters::defaultGTSAMIncRelinearizeThreshold();
	int skip = Parameters::defaultGTSAMIncRelinearizeSkip();
	Parameters::parse(parameters, Parameters::kGTSAMIncremental(), incremental);
	Parameters::parse(parameters, Parameters::kGTSAMIncRelinearizeThreshold(), threshold);
	Parameters::parse(parameters, Parameters::kGTSAMIncRelinearizeSkip(), skip);
	UDEBUG("GTSAM %s=%d", Parameters::kGTSAMOptimizer().c_str(), internalOptimizerType_);
	UDEBUG("GTSAM %s=%d", Parameters::kGTSAMIncremental().c_str(), incremental?1:0);
	UDEBUG("GTSAM %s=%f", Parameters::kGTSAMIncRelinearizeThreshold().c_str(), threshold);
	UDEBUG("GTSAM %s=%d", Parameters::kGTSAMIncRelinearizeSkip().c_str(), skip);
	if(incremental && !isam2_)
	{
		gtsam::ISAM2Params::OptimizationParams optParams;
		if(internalOptimizerType_==2)
		{
			optParams = gtsam::ISAM2DoglegParams();
		}
		else
		{
			optParams = gtsam::ISAM2GaussNewtonParams();
		}
		gtsam::ISAM2Params params(optParams);
		params.relinearizeThreshold = threshold;
		params.relinearizeSkip = skip;
		params.evaluateNonlinearError = true;
		isam2_ = new ISAM2(params);

		addedPoses_.clear();
		lastAddedConstraints_.clear();
		lastRootFactorIndex_.first = 0;
		lastSwitchId_ = 1000000000;
	}
	else if(!incremental && isam2_)
	{
		delete isam2_;
		isam2_ = 0;
	}
#endif
}

std::map<int, Transform> OptimizerGTSAM::optimize(
		int rootId,
		const std::map<int, Transform> & poses,
		const std::multimap<int, Link> & edgeConstraints,
		cv::Mat & outputCovariance,
		std::list<std::map<int, Transform> > * intermediateGraphes,
		double * finalError,
		int * iterationsDone)
{
	outputCovariance = cv::Mat::eye(6,6,CV_64FC1);
	std::map<int, Transform> optimizedPoses;
#ifdef RTABMAP_GTSAM

#ifndef RTABMAP_VERTIGO
	if(this->isRobust())
	{
		UWARN("Vertigo robust optimization is not available! Robust optimization is now disabled.");
		setRobust(false);
	}
#endif

	UDEBUG("Optimizing graph...");
	if(edgeConstraints.size()>=1 && poses.size()>=2 && iterations() > 0)
	{
		gtsam::NonlinearFactorGraph graph;

		// detect if there is a global pose prior set, if so remove rootId
		bool hasGPSPrior = false;
		bool hasGravityConstraints = false;
		if(!priorsIgnored() || (!isSlam2d() && gravitySigma() > 0))
		{
			for(std::multimap<int, Link>::const_iterator iter=edgeConstraints.begin(); iter!=edgeConstraints.end(); ++iter)
			{
				if(iter->second.from() == iter->second.to())
				{
					if(!priorsIgnored() && iter->second.type() == Link::kPosePrior)
					{
						hasGPSPrior = true;
						if ((isSlam2d() && 1 / static_cast<double>(iter->second.infMatrix().at<double>(5,5)) < 9999) ||
							(1 / static_cast<double>(iter->second.infMatrix().at<double>(3,3)) < 9999.0 &&
							 1 / static_cast<double>(iter->second.infMatrix().at<double>(4,4)) < 9999.0 &&
							 1 / static_cast<double>(iter->second.infMatrix().at<double>(5,5)) < 9999.0))
						{
							// orientation is set, don't set root prior (it is no GPS)
							rootId = 0;
							hasGPSPrior = false;
							break;
						}
					}
					if(iter->second.type() == Link::kGravity)
					{
						hasGravityConstraints = true;
						if(priorsIgnored())
						{
							break;
						}
					}
				}
			}
		}

		std::vector<ConstraintToFactor> addedPrior;
		gtsam::FactorIndices removeFactorIndices;

		//prior first pose
		if(rootId != 0 && (!isam2_ || lastRootFactorIndex_.first != rootId))
		{
			UDEBUG("Setting prior for rootId=%d", rootId);
			UASSERT(uContains(poses, rootId));
			const Transform & initialPose = poses.at(rootId);
			UDEBUG("hasGPSPrior=%s", hasGPSPrior?"true":"false");
			if(isSlam2d())
			{
				gtsam::noiseModel::Diagonal::shared_ptr priorNoise = gtsam::noiseModel::Diagonal::Variances(gtsam::Vector3(0.01, 0.01, hasGPSPrior?1e-2:std::numeric_limits<double>::min()));
				graph.add(gtsam::PriorFactor<gtsam::Pose2>(rootId, gtsam::Pose2(initialPose.x(), initialPose.y(), initialPose.theta()), priorNoise));
				addedPrior.push_back(ConstraintToFactor(rootId, rootId, -1));
			}
			else
			{
				gtsam::noiseModel::Diagonal::shared_ptr priorNoise = gtsam::noiseModel::Diagonal::Variances(
						(gtsam::Vector(6) <<
								(hasGravityConstraints?2:1e-2), (hasGravityConstraints?2:1e-2), hasGPSPrior?1e-2:std::numeric_limits<double>::min(), // roll, pitch, fixed yaw if there are no priors
								(hasGPSPrior?2:1e-2), hasGPSPrior?2:1e-2, hasGPSPrior?2:1e-2 // xyz
								).finished());
				graph.add(gtsam::PriorFactor<gtsam::Pose3>(rootId, gtsam::Pose3(initialPose.toEigen4d()), priorNoise));
				addedPrior.push_back(ConstraintToFactor(rootId, rootId, -1));
			}
			if(isam2_ && lastRootFactorIndex_.first!=0)
			{
				if(uContains(poses, lastRootFactorIndex_.first))
				{
					UDEBUG("isam2: switching rootid from %d to %d", lastRootFactorIndex_.first, rootId);
					removeFactorIndices.push_back(lastRootFactorIndex_.second);
				}
				else
				{
					UDEBUG("isam2: reset iSAM2, disjoint mapping sessions between previous root %d and new root %d", lastRootFactorIndex_.first, rootId);
					// reset iSAM2, disjoint mapping session
					gtsam::ISAM2Params params = isam2_->params();
					delete isam2_;
					isam2_ = new gtsam::ISAM2(params);
					addedPoses_.clear();
					lastAddedConstraints_.clear();
					lastRootFactorIndex_.first = 0;
					lastSwitchId_ = 1000000000;
				}
				lastRootFactorIndex_.first = 0;
			}
		}

		std::map<int, Transform> newPoses;
		std::multimap<int, Link> newEdgeConstraints;

		if(isam2_)
		{
			UDEBUG("Add new poses...");
			// new poses?
			for(std::map<int, Transform>::const_iterator iter=poses.begin(); iter!=poses.end(); ++iter)
			{
				if(addedPoses_.find(iter->first) == addedPoses_.end())
				{
					newPoses.insert(*iter);
					UDEBUG("Adding pose %d to factor graph", iter->first);
				}
			}
			UDEBUG("Add new links...");
			// new links?
			for(std::multimap<int, Link>::const_iterator iter=edgeConstraints.begin(); iter!=edgeConstraints.end(); ++iter)
			{
				if(addedPoses_.find(iter->second.from()) == addedPoses_.end() ||
				   addedPoses_.find(iter->second.to()) == addedPoses_.end())
				{
					newEdgeConstraints.insert(*iter);
					UDEBUG("Adding constraint %d (%d->%d) to factor graph", iter->first, iter->second.from(), iter->second.to());
				}
			}

			if(!this->isRobust())
			{
				UDEBUG("Remove links...");
				// Remove constraints not there anymore in case the last loop closures were rejected.
				// As we don't track "switch" constraints, we don't support this if vertigo is used.
				for(size_t i=0; i<lastAddedConstraints_.size(); ++i)
				{
					if(lastAddedConstraints_[i].from != lastAddedConstraints_[i].to &&
					   graph::findLink(edgeConstraints, lastAddedConstraints_[i].from, lastAddedConstraints_[i].to) == edgeConstraints.end())
					{
						removeFactorIndices.push_back(lastAddedConstraints_[i].factorIndice);
						UDEBUG("Removing constraint %d->%d (factor indice=%ld)",
								lastAddedConstraints_[i].from,
								lastAddedConstraints_[i].to,
								lastAddedConstraints_[i].factorIndice);
					}
				}
			}
			else if(poses.rbegin()->first >= 1000000000)
			{
				UERROR("Lastest pose id (%d) is too huge for robust optimization (over switch offset of 1000000000)", poses.rbegin()->first);
				return optimizedPoses;
			}

			lastAddedConstraints_ = addedPrior;
		}
		else
		{
			newPoses = poses;
			newEdgeConstraints = edgeConstraints;
		}

		UDEBUG("fill poses to gtsam... rootId=%d (priorsIgnored=%d landmarksIgnored=%d)",
				rootId, priorsIgnored()?1:0, landmarksIgnored()?1:0);
		gtsam::Values initialEstimate;
		std::map<int, bool> isLandmarkWithRotation;
		for(std::map<int, Transform>::const_iterator iter = newPoses.begin(); iter!=newPoses.end(); ++iter)
		{
			UASSERT(!iter->second.isNull());
			if(isSlam2d())
			{
				if(iter->first > 0)
				{
					initialEstimate.insert(iter->first, gtsam::Pose2(iter->second.x(), iter->second.y(), iter->second.theta()));
					addedPoses_.insert(iter->first);
				}
				else if(!landmarksIgnored())
				{
					// check if it is SE2 or only PointXY
					std::multimap<int, Link>::const_iterator jter=newEdgeConstraints.find(iter->first);
					UASSERT_MSG(jter != newEdgeConstraints.end(), uFormat("Not found landmark %d in edges!", iter->first).c_str());

					if (1 / static_cast<double>(jter->second.infMatrix().at<double>(5,5)) >= 9999.0)
					{
						initialEstimate.insert(iter->first, gtsam::Point2(iter->second.x(), iter->second.y()));
						isLandmarkWithRotation.insert(std::make_pair(iter->first, false));
					}
					else
					{
						initialEstimate.insert(iter->first, gtsam::Pose2(iter->second.x(), iter->second.y(), iter->second.theta()));
						isLandmarkWithRotation.insert(std::make_pair(iter->first, true));
					}
					addedPoses_.insert(iter->first);
				}

			}
			else
			{
				if(iter->first > 0)
				{
					initialEstimate.insert(iter->first, gtsam::Pose3(iter->second.toEigen4d()));
					addedPoses_.insert(iter->first);
				}
				else if(!landmarksIgnored())
				{
					// check if it is SE3 or only PointXYZ
					std::multimap<int, Link>::const_iterator jter=newEdgeConstraints.find(iter->first);
					UASSERT_MSG(jter != newEdgeConstraints.end(), uFormat("Not found landmark %d in edges!", iter->first).c_str());

					if (1 / static_cast<double>(jter->second.infMatrix().at<double>(3,3)) >= 9999.0 ||
						1 / static_cast<double>(jter->second.infMatrix().at<double>(4,4)) >= 9999.0 ||
						1 / static_cast<double>(jter->second.infMatrix().at<double>(5,5)) >= 9999.0)
					{
						initialEstimate.insert(iter->first, gtsam::Point3(iter->second.x(), iter->second.y(), iter->second.z()));
						isLandmarkWithRotation.insert(std::make_pair(iter->first, false));
					}
					else
					{
						initialEstimate.insert(iter->first, gtsam::Pose3(iter->second.toEigen4d()));
						isLandmarkWithRotation.insert(std::make_pair(iter->first, true));
					}
					addedPoses_.insert(iter->first);
				}
			}
		}

		UDEBUG("fill edges to gtsam...");
		if(!isam2_)
		{
			lastSwitchId_ = newPoses.rbegin()->first+1;
		}
		for(std::multimap<int, Link>::const_iterator iter=newEdgeConstraints.begin(); iter!=newEdgeConstraints.end(); ++iter)
		{
			int id1 = iter->second.from();
			int id2 = iter->second.to();

            UASSERT_MSG(poses.find(id1)!=poses.end(), uFormat("id1=%d", id1).c_str());
            UASSERT_MSG(poses.find(id2)!=poses.end(), uFormat("id2=%d", id2).c_str());

			UASSERT(!iter->second.transform().isNull());
			if(id1 == id2)
			{
				if(iter->second.type() == Link::kPosePrior && !priorsIgnored() &&
				  (!landmarksIgnored() || id1>0))
				{
					if(isSlam2d())
					{
						if(id1 < 0 && !isLandmarkWithRotation.at(id1))
						{
							noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Variances(Vector2(
									1/iter->second.infMatrix().at<double>(0,0),
									1/iter->second.infMatrix().at<double>(1,1)));
							graph.add(XYFactor<gtsam::Point2>(id1, gtsam::Point2(iter->second.transform().x(), iter->second.transform().y()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
						else if (1 / static_cast<double>(iter->second.infMatrix().at<double>(5,5)) >= 9999.0)
						{
							noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Variances(Vector2(
									1/iter->second.infMatrix().at<double>(0,0),
									1/iter->second.infMatrix().at<double>(1,1)));
							graph.add(XYFactor<gtsam::Pose2>(id1, gtsam::Point2(iter->second.transform().x(), iter->second.transform().y()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
						else
						{
							Eigen::Matrix<double, 3, 3> information = Eigen::Matrix<double, 3, 3>::Identity();
							if(!isCovarianceIgnored())
							{
								information(0,0) = iter->second.infMatrix().at<double>(0,0); // x-x
								information(0,1) = iter->second.infMatrix().at<double>(0,1); // x-y
								information(0,2) = iter->second.infMatrix().at<double>(0,5); // x-theta
								information(1,0) = iter->second.infMatrix().at<double>(1,0); // y-x
								information(1,1) = iter->second.infMatrix().at<double>(1,1); // y-y
								information(1,2) = iter->second.infMatrix().at<double>(1,5); // y-theta
								information(2,0) = iter->second.infMatrix().at<double>(5,0); // theta-x
								information(2,1) = iter->second.infMatrix().at<double>(5,1); // theta-y
								information(2,2) = iter->second.infMatrix().at<double>(5,5); // theta-theta
							}

							gtsam::noiseModel::Gaussian::shared_ptr model = gtsam::noiseModel::Gaussian::Information(information);
							graph.add(gtsam::PriorFactor<gtsam::Pose2>(id1, gtsam::Pose2(iter->second.transform().x(), iter->second.transform().y(), iter->second.transform().theta()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
					}
					else
					{
						if(id1 < 0 && !isLandmarkWithRotation.at(id1))
						{
							noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Precisions(Vector3(
										iter->second.infMatrix().at<double>(0,0),
										iter->second.infMatrix().at<double>(1,1),
										iter->second.infMatrix().at<double>(2,2)));
							graph.add(XYZFactor<gtsam::Point3>(id1, gtsam::Point3(iter->second.transform().x(), iter->second.transform().y(), iter->second.transform().z()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
						else if (1 / static_cast<double>(iter->second.infMatrix().at<double>(3,3)) >= 9999.0 ||
							1 / static_cast<double>(iter->second.infMatrix().at<double>(4,4)) >= 9999.0 ||
							1 / static_cast<double>(iter->second.infMatrix().at<double>(5,5)) >= 9999.0)
						{
							noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Precisions(Vector3(
										iter->second.infMatrix().at<double>(0,0),
										iter->second.infMatrix().at<double>(1,1),
										iter->second.infMatrix().at<double>(2,2)));
							graph.add(XYZFactor<gtsam::Pose3>(id1, gtsam::Point3(iter->second.transform().x(), iter->second.transform().y(), iter->second.transform().z()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
						else
						{
							Eigen::Matrix<double, 6, 6> information = Eigen::Matrix<double, 6, 6>::Identity();
							if(!isCovarianceIgnored())
							{
								memcpy(information.data(), iter->second.infMatrix().data, iter->second.infMatrix().total()*sizeof(double));
							}

							Eigen::Matrix<double, 6, 6> mgtsam = Eigen::Matrix<double, 6, 6>::Identity();
							mgtsam.block(0,0,3,3) = information.block(3,3,3,3); // cov rotation
							mgtsam.block(3,3,3,3) = information.block(0,0,3,3); // cov translation
							mgtsam.block(0,3,3,3) = information.block(3,0,3,3); // off diagonal
							mgtsam.block(3,0,3,3) = information.block(0,3,3,3); // off diagonal
							gtsam::SharedNoiseModel model = gtsam::noiseModel::Gaussian::Information(mgtsam);

							graph.add(gtsam::PriorFactor<gtsam::Pose3>(id1, gtsam::Pose3(iter->second.transform().toEigen4d()), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id1, -1));
						}
					}
				}
				else if(!isSlam2d() && gravitySigma() > 0 && iter->second.type() == Link::kGravity && newPoses.find(iter->first) != newPoses.end())
				{
					Vector3 r = gtsam::Pose3(iter->second.transform().toEigen4d()).rotation().xyz();
					gtsam::Unit3 nG = gtsam::Rot3::RzRyRx(r.x(), r.y(), 0).rotate(gtsam::Unit3(0,0,-1));
					gtsam::SharedNoiseModel model = gtsam::noiseModel::Isotropic::Sigmas(gtsam::Vector2(gravitySigma(), 10));
					graph.add(Pose3GravityFactor(iter->first, nG, model, Unit3(0,0,1)));
					lastAddedConstraints_.push_back(ConstraintToFactor(iter->first, iter->first, -1));
				}
			}
			else if(id1<0 || id2 < 0)
			{
				if(!landmarksIgnored())
				{
					//landmarks
					UASSERT((id1 < 0 && id2 > 0) || (id1 > 0 && id2 < 0));
					Transform t;
					if(id2 < 0)
					{
						t = iter->second.transform();
					}
					else
					{
						t = iter->second.transform().inverse();
						std::swap(id1, id2); // should be node -> landmark
					}

#ifdef RTABMAP_VERTIGO
					if(this->isRobust() && isLandmarkWithRotation.at(id2))
					{
						// create new switch variable
						// Sunderhauf IROS 2012:
						// "Since it is reasonable to initially accept all loop closure constraints,
						//  a proper and convenient initial value for all switch variables would be
						//  sij = 1 when using the linear switch function"
						double prior = 1.0;
						initialEstimate.insert(gtsam::Symbol('s',lastSwitchId_), vertigo::SwitchVariableLinear(prior));

						// create switch prior factor
						// "If the front-end is not able to assign sound individual values
						//  for Ξij , it is save to set all Ξij = 1, since this value is close
						//  to the individual optimal choice of Ξij for a large range of
						//  outliers."
						gtsam::noiseModel::Diagonal::shared_ptr switchPriorModel = gtsam::noiseModel::Diagonal::Sigmas(gtsam::Vector1(1.0));
						graph.add(gtsam::PriorFactor<vertigo::SwitchVariableLinear> (gtsam::Symbol('s',lastSwitchId_), vertigo::SwitchVariableLinear(prior), switchPriorModel));
					}
					else if(this->isRobust() && !isLandmarkWithRotation.at(id2))
					{
						UWARN("%s cannot be used for landmark constraints without orientation.", Parameters::kOptimizerRobust().c_str());
					}
#endif

					if(isSlam2d())
					{
						if(isLandmarkWithRotation.at(id2))
						{
							Eigen::Matrix<double, 3, 3> information = Eigen::Matrix<double, 3, 3>::Identity();
							if(!isCovarianceIgnored())
							{
								information(0,0) = iter->second.infMatrix().at<double>(0,0); // x-x
								information(0,1) = iter->second.infMatrix().at<double>(0,1); // x-y
								information(0,2) = iter->second.infMatrix().at<double>(0,5); // x-theta
								information(1,0) = iter->second.infMatrix().at<double>(1,0); // y-x
								information(1,1) = iter->second.infMatrix().at<double>(1,1); // y-y
								information(1,2) = iter->second.infMatrix().at<double>(1,5); // y-theta
								information(2,0) = iter->second.infMatrix().at<double>(5,0); // theta-x
								information(2,1) = iter->second.infMatrix().at<double>(5,1); // theta-y
								information(2,2) = iter->second.infMatrix().at<double>(5,5); // theta-theta
							}
							gtsam::noiseModel::Gaussian::shared_ptr model = gtsam::noiseModel::Gaussian::Information(information);

#ifdef RTABMAP_VERTIGO
							if(this->isRobust())
							{
								// create switchable edge factor
								graph.add(vertigo::BetweenFactorSwitchableLinear<gtsam::Pose2>(id1, id2, gtsam::Symbol('s', lastSwitchId_++), gtsam::Pose2(t.x(), t.y(), t.theta()), model));
							}
							else
#endif
							{
								graph.add(gtsam::BetweenFactor<gtsam::Pose2>(id1, id2, gtsam::Pose2(t.x(), t.y(), t.theta()), model));
								lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
							}
						}
						else
						{
							Eigen::Matrix<double, 2, 2> information = Eigen::Matrix<double, 2, 2>::Identity();
							if(!isCovarianceIgnored())
							{
								cv::Mat linearCov = cv::Mat(iter->second.infMatrix(), cv::Range(0,2), cv::Range(0,2)).clone();;
								memcpy(information.data(), linearCov.data, linearCov.total()*sizeof(double));
							}
							gtsam::SharedNoiseModel model = gtsam::noiseModel::Gaussian::Information(information);

							gtsam::Point2 landmark(t.x(), t.y());
							gtsam::Pose2 p;
							graph.add(gtsam::BearingRangeFactor<gtsam::Pose2, gtsam::Point2>(id1, id2, p.bearing(landmark), p.range(landmark), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
						}
					}
					else
					{
						if(isLandmarkWithRotation.at(id2))
						{
							Eigen::Matrix<double, 6, 6> information = Eigen::Matrix<double, 6, 6>::Identity();
							if(!isCovarianceIgnored())
							{
								memcpy(information.data(), iter->second.infMatrix().data, iter->second.infMatrix().total()*sizeof(double));
							}

							Eigen::Matrix<double, 6, 6> mgtsam = Eigen::Matrix<double, 6, 6>::Identity();
							mgtsam.block(0,0,3,3) = information.block(3,3,3,3); // cov rotation
							mgtsam.block(3,3,3,3) = information.block(0,0,3,3); // cov translation
							mgtsam.block(0,3,3,3) = information.block(3,0,3,3); // off diagonal
							mgtsam.block(3,0,3,3) = information.block(0,3,3,3); // off diagonal
							gtsam::SharedNoiseModel model = gtsam::noiseModel::Gaussian::Information(mgtsam);

#ifdef RTABMAP_VERTIGO
							if(this->isRobust() &&
							   iter->second.type() != Link::kNeighbor &&
							   iter->second.type() != Link::kNeighborMerged)
							{
								// create switchable edge factor
								graph.add(vertigo::BetweenFactorSwitchableLinear<gtsam::Pose3>(id1, id2, gtsam::Symbol('s', lastSwitchId_++), gtsam::Pose3(t.toEigen4d()), model));
							}
							else
#endif
							{
								graph.add(gtsam::BetweenFactor<gtsam::Pose3>(id1, id2, gtsam::Pose3(t.toEigen4d()), model));
								lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
							}
						}
						else
						{
							Eigen::Matrix<double, 3, 3> information = Eigen::Matrix<double, 3, 3>::Identity();
							if(!isCovarianceIgnored())
							{
								cv::Mat linearCov = cv::Mat(iter->second.infMatrix(), cv::Range(0,3), cv::Range(0,3)).clone();;
								memcpy(information.data(), linearCov.data, linearCov.total()*sizeof(double));
							}
							gtsam::SharedNoiseModel model = gtsam::noiseModel::Gaussian::Information(information);

							gtsam::Point3 landmark(t.x(), t.y(), t.z());
							gtsam::Pose3 p;
							graph.add(gtsam::BearingRangeFactor<gtsam::Pose3, gtsam::Point3>(id1, id2, p.bearing(landmark), p.range(landmark), model));
							lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
						}
					}
				}
			}
			else // id1 != id2
			{
#ifdef RTABMAP_VERTIGO
				if(this->isRobust() &&
				   iter->second.type() != Link::kNeighbor &&
				   iter->second.type() != Link::kNeighborMerged)
				{
					// create new switch variable
					// Sunderhauf IROS 2012:
					// "Since it is reasonable to initially accept all loop closure constraints,
					//  a proper and convenient initial value for all switch variables would be
					//  sij = 1 when using the linear switch function"
					double prior = 1.0;
					initialEstimate.insert(gtsam::Symbol('s',lastSwitchId_), vertigo::SwitchVariableLinear(prior));

					// create switch prior factor
					// "If the front-end is not able to assign sound individual values
					//  for Ξij , it is save to set all Ξij = 1, since this value is close
					//  to the individual optimal choice of Ξij for a large range of
					//  outliers."
					gtsam::noiseModel::Diagonal::shared_ptr switchPriorModel = gtsam::noiseModel::Diagonal::Sigmas(gtsam::Vector1(1.0));
					graph.add(gtsam::PriorFactor<vertigo::SwitchVariableLinear> (gtsam::Symbol('s',lastSwitchId_), vertigo::SwitchVariableLinear(prior), switchPriorModel));
				}
#endif
				if(isSlam2d())
				{
					Eigen::Matrix<double, 3, 3> information = Eigen::Matrix<double, 3, 3>::Identity();
					if(!isCovarianceIgnored())
					{
						information(0,0) = iter->second.infMatrix().at<double>(0,0); // x-x
						information(0,1) = iter->second.infMatrix().at<double>(0,1); // x-y
						information(0,2) = iter->second.infMatrix().at<double>(0,5); // x-theta
						information(1,0) = iter->second.infMatrix().at<double>(1,0); // y-x
						information(1,1) = iter->second.infMatrix().at<double>(1,1); // y-y
						information(1,2) = iter->second.infMatrix().at<double>(1,5); // y-theta
						information(2,0) = iter->second.infMatrix().at<double>(5,0); // theta-x
						information(2,1) = iter->second.infMatrix().at<double>(5,1); // theta-y
						information(2,2) = iter->second.infMatrix().at<double>(5,5); // theta-theta
					}
					gtsam::noiseModel::Gaussian::shared_ptr model = gtsam::noiseModel::Gaussian::Information(information);

#ifdef RTABMAP_VERTIGO
					if(this->isRobust() &&
					   iter->second.type()!=Link::kNeighbor &&
					   iter->second.type() != Link::kNeighborMerged)
					{
						// create switchable edge factor
						graph.add(vertigo::BetweenFactorSwitchableLinear<gtsam::Pose2>(id1, id2, gtsam::Symbol('s', lastSwitchId_++), gtsam::Pose2(iter->second.transform().x(), iter->second.transform().y(), iter->second.transform().theta()), model));
					}
					else
#endif
					{
						graph.add(gtsam::BetweenFactor<gtsam::Pose2>(id1, id2, gtsam::Pose2(iter->second.transform().x(), iter->second.transform().y(), iter->second.transform().theta()), model));
						lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
					}
				}
				else
				{
					Eigen::Matrix<double, 6, 6> information = Eigen::Matrix<double, 6, 6>::Identity();
					if(!isCovarianceIgnored())
					{
						memcpy(information.data(), iter->second.infMatrix().data, iter->second.infMatrix().total()*sizeof(double));
					}

					Eigen::Matrix<double, 6, 6> mgtsam = Eigen::Matrix<double, 6, 6>::Identity();
					mgtsam.block(0,0,3,3) = information.block(3,3,3,3); // cov rotation
					mgtsam.block(3,3,3,3) = information.block(0,0,3,3); // cov translation
					mgtsam.block(0,3,3,3) = information.block(3,0,3,3); // off diagonal
					mgtsam.block(3,0,3,3) = information.block(0,3,3,3); // off diagonal
					gtsam::SharedNoiseModel model = gtsam::noiseModel::Gaussian::Information(mgtsam);

#ifdef RTABMAP_VERTIGO
					if(this->isRobust() &&
					   iter->second.type() != Link::kNeighbor &&
					   iter->second.type() != Link::kNeighborMerged)
					{
						// create switchable edge factor
						graph.add(vertigo::BetweenFactorSwitchableLinear<gtsam::Pose3>(id1, id2, gtsam::Symbol('s', lastSwitchId_++), gtsam::Pose3(iter->second.transform().toEigen4d()), model));
					}
					else
#endif
					{
						graph.add(gtsam::BetweenFactor<gtsam::Pose3>(id1, id2, gtsam::Pose3(iter->second.transform().toEigen4d()), model));
						lastAddedConstraints_.push_back(ConstraintToFactor(id1, id2, -1));
					}
				}
			}
		}

		UDEBUG("create optimizer");
		gtsam::NonlinearOptimizer * optimizer = 0;

		if(!isam2_) // Batch optimization
		{
			UDEBUG("Batch optimization...");
			if(internalOptimizerType_ == 2)
			{
				gtsam::DoglegParams parameters;
				parameters.relativeErrorTol = epsilon();
				parameters.maxIterations = iterations();
				optimizer = new gtsam::DoglegOptimizer(graph, initialEstimate, parameters);
			}
			else if(internalOptimizerType_ == 1)
			{
				gtsam::GaussNewtonParams parameters;
				parameters.relativeErrorTol = epsilon();
				parameters.maxIterations = iterations();
				optimizer = new gtsam::GaussNewtonOptimizer(graph, initialEstimate, parameters);
			}
			else
			{
				gtsam::LevenbergMarquardtParams parameters;
				parameters.relativeErrorTol = epsilon();
				parameters.maxIterations = iterations();
				optimizer = new gtsam::LevenbergMarquardtOptimizer(graph, initialEstimate, parameters);
			}
		}
		else
		{
			UDEBUG("iSAM2 optimization...");
		}

		UDEBUG("GTSAM optimizing begin (max iterations=%d, robust=%d)", iterations(), isRobust()?1:0);
		UTimer timer;
		int it = 0;
		double initialError = optimizer?graph.error(initialEstimate):0;
		double lastError = optimizer?optimizer->error():0;
		for(int i=0; i<iterations(); ++i)
		{
			if(intermediateGraphes && i > 0)
			{
				float x,y,z,roll,pitch,yaw;
				std::map<int, Transform> tmpPoses;
				const Values values = isam2_?isam2_->calculateEstimate():optimizer->values();
#if GTSAM_VERSION_NUMERIC >= 40200
				for(gtsam::Values::deref_iterator iter=values.begin(); iter!=values.end(); ++iter)
#else
				for(gtsam::Values::const_iterator iter=values.begin(); iter!=values.end(); ++iter)
#endif
				{
					int key = (int)iter->key;
					if(iter->value.dim() > 1 && uContains(newPoses, key))
					{
						if(isSlam2d())
						{
							if(key > 0)
							{
								gtsam::Pose2 p = iter->value.cast<gtsam::Pose2>();
								tmpPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), p.theta())));
							}
							else if(!landmarksIgnored() && isLandmarkWithRotation.find(key)!=isLandmarkWithRotation.end())
							{
								if(isLandmarkWithRotation.at(key))
								{
									newPoses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
									gtsam::Pose2 p = iter->value.cast<gtsam::Pose2>();
									tmpPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), z, roll, pitch, p.theta())));
								}
								else
								{
									newPoses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
									gtsam::Point2 p = iter->value.cast<gtsam::Point2>();
									tmpPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), z, roll,pitch,yaw)));
								}
							}
						}
						else
						{
							if(key > 0)
							{
								gtsam::Pose3 p = iter->value.cast<gtsam::Pose3>();
								tmpPoses.insert(std::make_pair(key, Transform::fromEigen4d(p.matrix())));
							}
							else if(!landmarksIgnored() && isLandmarkWithRotation.find(key)!=isLandmarkWithRotation.end())
							{
								if(isLandmarkWithRotation.at(key))
								{
									gtsam::Pose3 p = iter->value.cast<gtsam::Pose3>();
									tmpPoses.insert(std::make_pair(key, Transform::fromEigen4d(p.matrix())));
								}
								else
								{
									newPoses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
									gtsam::Point3 p = iter->value.cast<gtsam::Point3>();
									tmpPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), p.z(), roll,pitch,yaw)));
								}
							}
						}
					}
				}
				intermediateGraphes->push_back(tmpPoses);
			}

			gtsam::ISAM2Result result;
			double error = 0;
			try
			{
				if(optimizer) // Batch optimization
				{
					optimizer->iterate();
					error = optimizer->error();
				}
				else if(i==0) // iSAM2 (add factors)
				{
					UDEBUG("Update iSAM with the new factors");
					result = isam2_->update(graph, initialEstimate, removeFactorIndices);
#if BOOST_VERSION >= 106800
					UASSERT(result.errorBefore.has_value());
					UASSERT(result.errorAfter.has_value());
#else
					UASSERT(result.errorBefore.is_initialized());
					UASSERT(result.errorAfter.is_initialized());
#endif
					UDEBUG("error before = %f after=%f", result.errorBefore.value(), result.errorAfter.value());
					initialError = lastError = result.errorBefore.value();
					error = result.errorAfter.value();
					if(!this->isRobust())
					{
						UASSERT_MSG(lastAddedConstraints_.size() == result.newFactorsIndices.size(),
								uFormat("%ld versus %ld", lastAddedConstraints_.size(), result.newFactorsIndices.size()).c_str());
						for(size_t j=0; j<result.newFactorsIndices.size(); ++j)
						{
							UDEBUG("New factor indice: %ld", result.newFactorsIndices[j]);
							lastAddedConstraints_[j].factorIndice = result.newFactorsIndices[j];
						}
					}
					if(rootId != 0 && lastRootFactorIndex_.first == 0)
					{
						UASSERT(result.newFactorsIndices.size()>=1);
						lastRootFactorIndex_.first = rootId;
						lastRootFactorIndex_.second = result.newFactorsIndices[0]; // first one should be always the root prior
					}
				}
				else // iSAM2 (more iterations)
				{
					result = isam2_->update();
#if BOOST_VERSION >= 106800
					UASSERT(result.errorBefore.has_value());
					UASSERT(result.errorAfter.has_value());
#else
					UASSERT(result.errorBefore.is_initialized());
					UASSERT(result.errorAfter.is_initialized());
#endif
					UDEBUG("error before = %f after=%f", result.errorBefore.value(), result.errorAfter.value());

					lastError = result.errorBefore.value();
					error = result.errorAfter.value();
				}
				++it;
			}
			catch(gtsam::IndeterminantLinearSystemException & e)
			{
				UWARN("GTSAM exception caught: %s\n Graph has %d edges and %d vertices", e.what(),
						(int)newEdgeConstraints.size(),
						(int)newPoses.size());
				delete optimizer;
				if(isam2_)
				{
					// We are in bad state, cleanup
					UDEBUG("Reset iSAM2!");
					gtsam::ISAM2Params params = isam2_->params();
					delete isam2_;
					isam2_ = new gtsam::ISAM2(params);
					addedPoses_.clear();
					lastAddedConstraints_.clear();
					lastRootFactorIndex_.first = 0;
					lastSwitchId_ = 1000000000;
				}
				return optimizedPoses;
			}

			// early stop condition
			UDEBUG("iteration %d error =%f", i+1, error);
			double errorDelta = lastError - error;
			if((isam2_ || i>0) && errorDelta < this->epsilon())
			{
				if(errorDelta < 0)
				{
					UDEBUG("Negative improvement?! Ignore and continue optimizing... (%f < %f)", errorDelta, this->epsilon());
				}
				else
				{
					UDEBUG("Stop optimizing, not enough improvement (%f < %f)", errorDelta, this->epsilon());
					break;
				}
			}
			else if(i==0 && error < this->epsilon())
			{
				UINFO("Stop optimizing, error is already under epsilon (%f < %f)", error, this->epsilon());
				break;
			}
			lastError = error;
		}
		if(finalError)
		{
			*finalError = lastError;
		}
		if(iterationsDone)
		{
			*iterationsDone = it;
		}
		UDEBUG("GTSAM optimizing end (%d iterations done (error initial=%f final=%f), time=%f s)",
				it, initialError, lastError, timer.ticks());

		float x,y,z,roll,pitch,yaw;
		const gtsam::Values values = isam2_?isam2_->calculateEstimate():optimizer->values();
#if GTSAM_VERSION_NUMERIC >= 40200
		for(gtsam::Values::deref_iterator iter=values.begin(); iter!=values.end(); ++iter)
#else
		for(gtsam::Values::const_iterator iter=values.begin(); iter!=values.end(); ++iter)
#endif
		{
			int key = (int)iter->key;
			if(iter->value.dim() > 1 && uContains(poses, key))
			{
				if(isSlam2d())
				{
					if(key > 0)
					{
						poses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
						gtsam::Pose2 p = iter->value.cast<gtsam::Pose2>();
						optimizedPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), z, roll, pitch, p.theta())));
					}
					else if(!landmarksIgnored() && isLandmarkWithRotation.find(key)!=isLandmarkWithRotation.end())
					{
						if(isLandmarkWithRotation.at(key))
						{
							poses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
							gtsam::Pose2 p = iter->value.cast<gtsam::Pose2>();
							optimizedPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), z, roll, pitch, p.theta())));
						}
						else
						{
							poses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
							gtsam::Point2 p = iter->value.cast<gtsam::Point2>();
							optimizedPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), z,roll,pitch,yaw)));
						}
					}
				}
				else
				{
					if(key > 0)
					{
						gtsam::Pose3 p = iter->value.cast<gtsam::Pose3>();
						optimizedPoses.insert(std::make_pair(key, Transform::fromEigen4d(p.matrix())));
					}
					else if(!landmarksIgnored() && isLandmarkWithRotation.find(key)!=isLandmarkWithRotation.end())
					{
						if(isLandmarkWithRotation.at(key))
						{
							gtsam::Pose3 p = iter->value.cast<gtsam::Pose3>();
							optimizedPoses.insert(std::make_pair(key, Transform::fromEigen4d(p.matrix())));
						}
						else
						{
							poses.at(key).getTranslationAndEulerAngles(x,y,z,roll,pitch,yaw);
							gtsam::Point3 p = iter->value.cast<gtsam::Point3>();
							optimizedPoses.insert(std::make_pair(key, Transform(p.x(), p.y(), p.z(), roll,pitch,yaw)));
						}
					}
				}
			}
		}

		// compute marginals
		try {
			UDEBUG("Computing marginals for node %d...", poses.rbegin()->first);
			UTimer t;
			gtsam::Matrix info;
			if(optimizer)
			{
				gtsam::Marginals marginals(graph, optimizer->values());
			 	info = marginals.marginalCovariance(poses.rbegin()->first);
			}
			else //iSAM2
			{
				info = isam2_->marginalCovariance(poses.rbegin()->first);
			}
			UDEBUG("Computed marginals = %fs (key=%d)", t.ticks(), poses.rbegin()->first);
			if(isSlam2d() && info.cols() == 3 && info.cols() == 3)
			{
				outputCovariance.at<double>(0,0) = info(0,0); // x-x
				outputCovariance.at<double>(0,1) = info(0,1); // x-y
				outputCovariance.at<double>(0,5) = info(0,2); // x-theta
				outputCovariance.at<double>(1,0) = info(1,0); // y-x
				outputCovariance.at<double>(1,1) = info(1,1); // y-y
				outputCovariance.at<double>(1,5) = info(1,2); // y-theta
				outputCovariance.at<double>(5,0) = info(2,0); // theta-x
				outputCovariance.at<double>(5,1) = info(2,1); // theta-y
				outputCovariance.at<double>(5,5) = info(2,2); // theta-theta
			}
			else if(!isSlam2d() && info.cols() == 6 && info.cols() == 6)
			{
				Eigen::Matrix<double, 6, 6> mgtsam = Eigen::Matrix<double, 6, 6>::Identity();
				mgtsam.block(3,3,3,3) = info.block(0,0,3,3); // cov rotation
				mgtsam.block(0,0,3,3) = info.block(3,3,3,3); // cov translation
				mgtsam.block(0,3,3,3) = info.block(3,0,3,3); // off diagonal
				mgtsam.block(3,0,3,3) = info.block(0,3,3,3); // off diagonal
				memcpy(outputCovariance.data, mgtsam.data(), outputCovariance.total()*sizeof(double));
			}
			else
			{
				UERROR("GTSAM: Could not compute marginal covariance!");
				optimizedPoses.clear(); // Failed optimization
			}
		}
		catch(gtsam::IndeterminantLinearSystemException & e)
		{
			UERROR("GTSAM exception caught: %s", e.what());
			optimizedPoses.clear(); // Failed optimization
		}
		catch(std::exception& e)
		{
			UERROR("GTSAM exception caught: %s", e.what());
			optimizedPoses.clear(); // Failed optimization
		}

		delete optimizer;
	}
	else if(poses.size() == 1 || iterations() <= 0)
	{
		optimizedPoses = poses;
	}
	else
	{
		UWARN("This method should be called at least with 1 pose!");
	}
	UDEBUG("Optimizing graph...end!");
#else
	UERROR("Not built with GTSAM support!");
#endif
	return optimizedPoses;
}

} /* namespace rtabmap */
